Question

Explain what is meant by the following two terms used in molecular orbital theory. In both cases use molecular hydrogen (H2) to illustrate your answer. (G) LCAO (ii) HOMO ii) Differentiate between the LCAO Approximation 1 and LCAO 3 marks 3 marks Approximation 2. Illustrate how these two approximations pertain to the orbitals of the homonuclear molecules, di-borane () and di-fluorine (F2). Explain the origin of the different energy ordering of the molecular orbitals in these two molecules. 8 marks) b.) Calculate the standard entropy change AS for the following reaction at 25°C. Use the data provided in Table 1. (rhombic) + 02(g)-50209) 3 marks] Table 1 Compound 31.88 205.0 248.5 (ii) Provide a brief justification for the sign of the AS" of reaction you obtained. 3 marks (iii) Based on the data shown in Table 2 below Table 2 Compound Ethane (gas) Oxygen (gas) Carbon dioxide (gas) Water (liquid) 32.86 -394.4 237.2 Calculate the standard Gibbs free energy change (AG) for the combustion of ethane at 25°C 17 marks] MacBook Pro

Differentiate between the LCAO approximation 1 and LCAO approximation 2. Illustrate how these 2 approximations pertain to the orbitals of the homonuclear molecules diborane(Br2) and difluorine(F2). Explain the origin of the different energy ordering of the molecular orbitals in these two molecules.

Answer 1

MO theory takes the idea of atomic orbitals overlapping to a new level, where new molecular orbitals are generated using a mathematical process called linear combination of atomic orbitals (LCAO).

Molecular orbitals share many similarities with atomic orbitals:

–          They are filled from lowest energy to highest energy (Aufbau principle).

–          They can hold a maximum of two electrons of opposite spin per orbital (Pauli exclusion principle).

The major difference between atomic and molecular orbitals is that atomic orbitals represent electron density in space associated with a particular atom. Molecular orbitals are associated with the entire molecule, meaning the electron density is delocalized (spread out) over more than one atom.

The Molecular Orbitals of the Hydrogen Molecule

Combining the 1s orbitals of each hydrogen atom using LCAO, two molecular orbitals are generated σ1s (pronounced sigma one s) and σ*1s (pronounced sigma star one s).

The σ1s orbital is generated by a constructive combination (or interference), where the two atomic orbitals wave functions reinforce (add to) each other. This is the lower energy of the two molecular orbitals and is known as thebonding molecular orbital.

Generating molecular orbitals of molecules more complex than hydrogen using the LCAO method requires following a few additional guidelines:

–          The number of MOs generated is equal to the number of atomic orbitals combined.

–          Combined atomic orbitals should be of similar energy levels.

–          The effectiveness of atomic orbital combination depends on the amount of orbital overlap. Increased overlap lowers the energy of the bonding molecular orbital further, and raises the energy of the antibonding molecular orbital.

Lecture 2 Simple Molec (number of bonding electrons) (number of antibonding electronmount of bond order- bonding node zero electron density because of opposite phases LCAO-linear combination of atomic orbitals molecule H r Ơtzls, . ls-antibonding MO LUMO H higher less stable potential energy AE2 bond energy energy of isolated atoms lower more stable HOMO lsa + lsb-bonding MO Similar phase of electron density (no node) adds together constructively. LUMO lowest unoccupied molecular orbital HOMO highest occupied molecular orbital There is a big energy advantage for a hydrogen molecule over two hydrogen atoms bond order (H2 molecule):Lym lbond - Sigma (O) bonding molecular orbital-Shared electron density is directly between the bonding atoms, along the bonding axis. A sigma bonds is always the first bond formed between two atoms. Sigma star (e*) antibonding molecular orbital-Normally this orbital is empty, but if it should be occupied, the wave nature of electron density (when present) is out of phase (destructive interference) and canceling in nature. There is a node between the bonding atoms (zero electron density). Problem 1-What would the MO pictures of He2, H2, H2 and He2 look like? Would you expect that these species could exist? What would be their bond orders? node zero electron t bond LCAO linear combination of atomic orbitals density because of opposite phases 2p,-2p, antibonding MO- higher, less stable AE bond energy energy osolated porbitals energy 2p lower, more stable Overlap is above and below the bond axis, not directly between the bonded atoms HOMO 2p.2p bonding MO- LUMO lowest unoccupied molecular orbital HOMO highest occupied molecular orbital Similar phase of electron density (no node) adds together constructively There is a big energy adv pi bond over two isolated p 1 bondpi bond order of a pi bond